Monday, February 16, 2015

Aristotle laid out the principles of his logic in his writing Περὶ Ἑρμηνείας, in Latin De Interpretatione, in English On Exposition. It is a graphical representation of the relations between propositions that guarantee their truth. If philosophers and scientists would internalise the logical rules in Aristotle's square of opposition, a lot of misunderstandings would be prevented. SEE: The Square of Opposition as a Whiteboard animation

Sunday, February 08, 2015

Discussions of the nature of time, and of various issues related to time, have always featured prominently in philosophy, but they have been especially important since the beginning of the 20th Century. This article contains a brief overview of some of the main topics in the philosophy of time — Fatalism; Reductionism and Platonism with respect to time; the topology of time; McTaggart's arguments; The A Theory and The B Theory; Presentism, Eternalism, and The Growing Universe Theory; time travel; and the 3D/4D controversy — together with some suggestions for further reading on each topic, and a bibliography.Time Markosian, Ned, "Time", The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.), URL = .

If we believe time to be in relation to space-time, then the parameters of our thinking have a distinction about how we look at time?

Time is often referred to as the fourth dimension, along with the spatial dimensions. Time

So you see, one is being selective about the parameters they give them self with which to regard time.

Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy. Time

If we are part and parcel, then what said that any idea of continuity can express itself.
One would have to believe there is a perfect symmetry in existence that is expressed as an asymmetric example of such perfection, and maybe defined as the matters?

Immanuel Kant, in the Critique of Pure Reason, described time as an a priori intuition that allows us (together with the other a priori intuition, space) to comprehend sense experience.[60] With Kant, neither space nor time are conceived as substances, but rather both are elements of a systematic mental framework that necessarily structures the experiences of any rational agent, or observing subject. Kant thought of time as a fundamental part of an abstract conceptual framework, together with space and number, within which we sequence events, quantify their duration, and compare the motions of objects. In this view, time does not refer to any kind of entity that "flows," that objects "move through," or that is a "container" for events. Spatial measurements are used to quantify the extent of and distances between objects, and temporal measurements are used to quantify the durations of and between events. Time was designated by Kant as the purest possible schema of a pure concept or category.Time

All bold added for emphasis by me.

So, we may come to believe something about yourself that was not quite evident before until we acquiescent to the question regarding the nature of time as we have come to know them.

If you come to believe there are limits in terms of the reductionist efforts regarding measure, so as to be limited in our perceptions, then what lies beyond, that what we may measure? Do you know how to measure a thought?

But perhaps most significant is that all their observations are
compatible with relativity. At no point does the time machine-simulator
lead to grandfather-type paradoxes, regardless of the tricks it plays
with causality. That’s just as Deutsch predicted. See: The Quantum Experiment That Simulates A Time Machine

How would you perceive Time Dilation. How would you then perceive Time Travel. How would you perceive time variable measure? Given the constraints of such a measure, we have come "to believe" something in science.

In
philosophy, especially that of Aristotle, the golden mean is the
desirable middle between two extremes, one of excess and the other of
deficiency. -The Golden Mean (philosophy)

In
the Eudemian Ethics, Aristotle writes on the virtues. Aristotle’s
theory on virtue ethics is one that does not see a person’s actions as a
reflection of their ethics but rather looks into the character of a
person as the reason behind their ethics. His constant phrase is, "… is
the Middle state between …". His psychology of the soul and its virtues
is based on the golden mean between the extremes. In the Politics,
Aristotle criticizes the Spartan Polity by critiquing the
disproportionate elements of the constitution; e.g., they trained the
men and not the women, and they trained for war but not peace. This
disharmony produced difficulties which he elaborates on in his work. See
also the discussion in the Nicomachean Ethics of the golden mean, and
Aristotelian ethics in general.-http://en.wikipedia.org/wiki/Golden_mean_(philosophy)#Aristotle

Book VI of the Nicomachean Ethics is identical to Book V of the Eudemian Ethics. Earlier in both works, both the Nicomachean Ethics Book IV, and the equivalent book in the Eudemian Ethics (Book III), though different, ended by stating that the next step was to discuss justice. Indeed in Book I Aristotle set out his justification for beginning with particulars and building up to the highest things. Character virtues (apart from justice perhaps) were already discussed in an approximate way, as like achieving at middle point between two extreme options, but this now raises the question of how we know and recognize the things we aim at or avoid. Recognizing the mean recognizing the correct boundary-marker (horos) which defines the frontier of the mean. And so practical ethics, having a good character, requires knowledge.-

The nature of this distinction has been disputed by various philosophers; however, the terms may be roughly defined as follows:

A priori knowledge is knowledge that is known independently of experience (that is, it is non-empirical, or arrived at beforehand, usually by reason). It will henceforth be acquired through anything that is independent from experience.A posteriori knowledge is knowledge that is known by experience (that is, it is empirical, or arrived at afterward).

A priori knowledge is a way of gaining knowledge without the need of
experience. In Bruce Russell's article "A Priori Justification and
Knowledge"[19] he says that it is "knowledge based on a priori
justification," (1) which relies on intuition and the nature of these
intuitions. A priori knowledge is often contrasted with posteriori
knowledge, which is knowledge gained by experience. A way to look at the
difference between the two is through an example. Bruce Russell give
two proposition in which the reader decides which one he believes more.
Option A: All crows are birds. Option B: All crows are black. If you
believe option A, then you are a priori justified in believing it
because you don't have to see a crow to know it's a bird. If you believe
in option B, then you are posteriori justified to believe it because
you have seen many crows therefore knowing they are black. He goes on to
say that it doesn't matter if the statement is true or not, only that
if you believe in one or the other that matters.

The idea of a priori knowledge is that it is based on intuition or rational insights.
Laurence BonJour says in his article "The Structure of Empirical
Knowledge",[20] that a "rational insight is an immediate,
non-inferential grasp, apprehension or 'seeing' that some proposition is
necessarily true." (3) Going back to the crow example, by Laurence
BonJour's definition the reason you would believe in option A is because
you have an immediate knowledge that a crow is a bird, without ever
experiencing one.- Acquiring Knowledge

***

In
epistemology, rationalism is the view that "regards reason as the chief
source and test of knowledge"[1] or "any view appealing to reason as a
source of knowledge or justification".[2] More formally, rationalism is
defined as a methodology or a theory "in which the criterion of the
truth is not sensory but intellectual and deductive".[3] Rationalists
believe reality has an intrinsically logical structure. Because of this,
rationalists argue that certain truths exist and that the intellect can
directly grasp these truths. That is to say, rationalists assert that
certain rational principles exist in logic, mathematics, ethics, and
metaphysics that are so fundamentally true that denying them causes one
to fall into contradiction. Rationalists have such a high confidence in
reason that proof and physical evidence are unnecessary to ascertain
truth – in other words, "there are significant ways in which our
concepts and knowledge are gained independently of sense experience".[4]
Because of this belief, empiricism is one of rationalism's greatest
rivals. -Rationalism

Empiricism, often used by natural scientists, says that "knowledge is
based on experience" and that "knowledge is tentative and
probabilistic, subject to continued revision and falsification."[4] One of the epistemological tenets is that sensory experience creates knowledge. The scientific method, including experiments and validated measurement tools, guides empirical research.

In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms Mathematical proof

¬ negation (NOT) The tilde ( ˜ ) is also often used.∧ conjunction (AND) The ampersand ( & ) or dot ( · ) are also often used.∨ disjunction (OR) This is the inclusive disjunction, equivalent to and/or in English.⊕ exclusive disjunction (XOR) ⊕ means that only one of the connected propositions is true, equivalent to either…or. Sometimes ⊻ is used.| alternative denial (NAND) Means “not both”. Sometimes written as ↑↓ joint denial (NOR) Means “neither/nor”.→ conditional (if/then) Many logicians use the symbol ⊃ instead. This is also known as material implication.↔ biconditional (iff) Means “if and only if” ≡ is sometimes used, but this site reserves that symbol for equivalence.

Quantifiers

∀ universal quantifier Means “for all”, so ∀xPx means that Px is true for every x.∃ existential quantifier Means “there exists”, so ∃xPx means that Px is true for at least one x.Relations

⊨ implication α ⊨ β means that β follows from α≡ equivalence Also ⇔. Equivalence is two-way implication, so α ≡ β means α implies β and β implies α.⊢ provability Shows provable inference. α is provable β means that from α we can prove that β.∴ therefore Used to signify the conclusion of an argument. Usually taken to mean implication, but often used to present arguments in which the premises do not deductively imply the conclusion.⊩ forces A relationship between possible worlds and sentences in modal logic.Truth-Values

⊤ tautology May be used to replace any tautologous (always true) formula.⊥ contradiction May be used to replace any contradictory (always false) formula. Sometimes “F” is used.

Parentheses

( ) parentheses Used to group expressions to show precedence of operations. Square brackets

[ ] are sometimes used to clarify groupings.Set Theory

∈ membership Denotes membership in a set. If a ∈ Γ, then a is a member (or an element) of set Γ.∪ union Used to join sets. If S and T are sets of formula, S ∪ T is a set containing all members of both.∩ intersection The overlap between sets. If S and T are sets of formula, S ∩ T is a set containing those elemenets that are members of both.⊆ subset A subset is a set containing some or all elements of another set.⊂ proper subset A proper subset contains some, but not all, elements of another set.= set equality Two sets are equal if they contain exactly the same elements.∁ absolute complement ∁(S) is the set of all things that are not in the set S. Sometimes written as C(S), S or SC.- relative complement T - S is the set of all elements in T that are not also in S. Sometimes written as T \ S.∅ empty set The set containing no elements.

Modalities

□ necessarily Used only in modal logic systems. Sometimes expressed as [] where the symbol is unavailable.◊ possibly Used only in modal logic systems. Sometimes expressed as <> where the symbol is unavailable.

Propositions, Variables and Non-Logical Symbols

The use of variables in logic varies depending on the system and the author of the logic being presented. However, some common uses have emerged. For the sake of clarity, this site will use the system defined below.

x, y, z variables Lowercase Roman letters towards the end of the alphabet are used to signify variables. In logical systems, these are usually coupled with a quantifier, ∀ or ∃, in order to signify some or all of some unspecified subject or object. By convention, these begin with x, but any other letter may be used if needed, so long as they are defined as a variable by a quantifier.

a, b, c, … z constants Lowercase Roman letters, when not assigned by a quantifier, signifiy a constant, usually a proper noun. For instance, the letter “j” may be used to signify “Jerry”. Constants are given a meaning before they are used in logical expressions.

Ax, Bx … Zx predicate symbols Uppercase Roman letters appear again to indicate predicate relationships between variables and/or constants, coupled with one or more variable places which may be filled by variables or constants. For instance, we may definite the relation “x is green” as Gx, and “x likes y” as Lxy. To differentiate them from propositions, they are often presented in italics, so while P may be a proposition, Px is a predicate relation for x. Predicate symbols are non-logical — they describe relations but have neither operational function nor truth value in themselves.

Γ, Δ, … Ω sets of formulae Uppercase Greek letters are used, by convention, to refer to sets of formulae. Γ is usually used to represent the first site, since it is the first that does not look like Roman letters. (For instance, the uppercase Alpha (Α) looks identical to the Roman letter “A”)

Γ, Δ, … Ω possible worlds In modal logic, uppercase greek letters are also used to represent possible worlds. Alternatively, an uppercase W with a subscript numeral is sometimes used, representing worlds as W0, W1, and so on.

{ } sets Curly brackets are generally used when detailing the contents of a set, such as a set of formulae, or a set of possible worlds in modal logic. For instance, Γ = { α, β, γ, δ }

Contrary-
All S are P, No S is P
All s is P is contrary to the claim NO S is P.

-----------------------

A contrary can be true as well as false.
Contraries can both be false. Contraries can't both be true.

The A and E forms entail each other's negations

Subcontrary
Some S are P, Some S are not P

--------------------------------------------

Sub contraries can't both be false. Sub contraries can both be true.
The negation of the I form entails the (unnegated) E form, and vice versa.

Contradiction-
All S are P, Some S are not P,
Some S are P, No S are P

-----------------------------------

For contradictions -Two propositions are contradictory if they cannot both be true and they cannot both be false.
Contradictory means there is exactly one truth value and if one proposition is true the other MUST be false. If one is false the other MUST be true.

The propositions can't both be true and the propositions can't both be false.

The A and O forms entail each other's negations, as do the E and I forms.

The negation of the A form entails the (unnegated) O form, and vice versa; likewise for the E and I forms.Super alteration[-
Every S is P, implies Some S are P
No S is P, implies Some S are not P

--------------------------------------------

The two propositions can be true.

Sub alteration-
All S are P, Some S are P
No S are P, Some S are not P

----------------------------------

A proposition is a subaltern of another if it must be true
The A form entails the I form, and the E form entails the O form.

As in the first(Proposition 1) or the "I"
"To be clear the I proposition is SOME S is P. This is what is meant by a I proposition.
Well you can certainly infer if an I proposition is true that an E proposition is false because they are contradictory. Unfortunately there is NOTHING else to infer with certainty.
That is there will be times where the proposition will be true and different times it will be false.
This is called contingent truths. That is the proposition is not true 100% of the time. It has false cases. Deductive logic tries to stay away from contingent truths."

Universal statements are contraries: 'every man is just' and 'no man is just' cannot be true together, although one may be true and the other false, and also both may be false (if at least one man is just, and at least one man is not just).

Particular statements are subcontraries. 'Some man is just' and 'some man is not just' cannot be false together

The particular statement of one quality is the subaltern of the universal statement of that same quality, which is the superaltern of the particular statement, because in Aristotelian semantics 'every A is B' implies 'some A is B' and 'no A is B' implies 'some A is not B'. Note that modern formal interpretations of English sentences interpret 'every A is B' as 'for any x, x is A implies x is B', which does not imply 'some x is A'. This is a matter of semantic interpretation, however, and does not mean, as is sometimes claimed, that Aristotelian logic is 'wrong'.

The universal affirmative and the particular negative are contradictories. If some A is not B, not every A is B. Conversely, though this is not the case in modern semantics, it was thought that if every A is not B, some A is not B. This interpretation has caused difficulties (see below). While Aristotle's Greek does not represent the particular negative as 'some A is not B', but as 'not every A is B', someone in his commentary on the Peri hermaneias, renders the particular negative as 'quoddam A non est B', literally 'a certain A is not a B', and in all medieval writing on logic it is customary to represent the particular proposition in this way.

These relationships became the basis of a diagram originating with Boethius and used by medieval logicians to classify the logical relationships. The propositions are placed in the four corners of a square, and the relations represented as lines drawn between them, whence the name 'The Square of Opposition'.

The Hyper-Kamiokande project aims to address the mysteries of the origin
and evolution of the Universe's matter and to confront theories of
elementary particle unification. To realize these goals the project will
combine a high intensity neutrino beam from the Japan Proton
Accelerator Research Complex (J-PARC) with a new detector based upon
precision neutrino experimental techniques developed in Japan. The
Hyper-Kamiokande project will be about 25 times larger than
Super-Kamiokande, the research facility that was first to discover
evidence for neutrino mass in 1998. On this occasion, a research
proto-collaboration will be formed to advance the Hyper-Kamiokande
project internationally and a symposium will be held to commemorate and
promote the event. In addition, a signing ceremony marking an agreement
for the promotion of the project between the University of Tokyo
Institute for Cosmic Ray Research (ICRR) and the High Energy Accelerator
Research Organization (KEK) Institute of Particle and Nuclear Studies
will take place during the symposium. See: Hyper-Kamiokande

Thursday, February 05, 2015

University of Chicago
scientists can create an exotic, particle-like excitation
called a roton in superfluids with the tabletop apparatus pictured here.
Posing left to right are graduate students Li-Chung Ha and Logan Clark,
and Prof. Cheng Chin.

We present experimental evidence showing that an interacting Bose
condensate in a shaken optical lattice develops a roton-maxon excitation
spectrum, a feature normally associated with superfluid helium. The
roton-maxon feature originates from the double-well dispersion in the
shaken lattice, and can be controlled by both the atomic interaction and
the lattice modulation amplitude. We determine the excitation spectrum
using Bragg spectroscopy and measure the critical velocity by dragging a
weak speckle potential through the condensate—both techniques are based
on a digital micromirror device. Our dispersion measurements are in
good agreement with a modified Bogoliubov model. DOI: http://dx.doi.org/10.1103/PhysRevLett.114.055301